Optimal. Leaf size=15 \[ x^2 \left (a x^n\right )^{-1/n} \]
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Rubi [A] time = 0.0014573, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154, Rules used = {15, 8} \[ x^2 \left (a x^n\right )^{-1/n} \]
Antiderivative was successfully verified.
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Rule 15
Rule 8
Rubi steps
\begin{align*} \int x \left (a x^n\right )^{-1/n} \, dx &=\left (x \left (a x^n\right )^{-1/n}\right ) \int 1 \, dx\\ &=x^2 \left (a x^n\right )^{-1/n}\\ \end{align*}
Mathematica [A] time = 0.0013306, size = 15, normalized size = 1. \[ x^2 \left (a x^n\right )^{-1/n} \]
Antiderivative was successfully verified.
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Maple [F] time = 0.015, size = 0, normalized size = 0. \begin{align*} \int{\frac{x}{\sqrt [n]{a{x}^{n}}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.00403, size = 27, normalized size = 1.8 \begin{align*} \frac{x^{2}}{a^{\left (\frac{1}{n}\right )}{\left (x^{n}\right )}^{\left (\frac{1}{n}\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.75041, size = 15, normalized size = 1. \begin{align*} \frac{x}{a^{\left (\frac{1}{n}\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 2.0847, size = 56, normalized size = 3.73 \begin{align*} \begin{cases} a^{- \frac{1}{n}} x^{2} \left (x^{n}\right )^{- \frac{1}{n}} & \text{for}\: a \neq 0^{n} \\- \frac{x^{2}}{0^{n} \tilde{\infty }^{n} \left (0^{n}\right )^{\frac{1}{n}} \left (x^{n}\right )^{\frac{1}{n}} - 2 \left (0^{n}\right )^{\frac{1}{n}} \left (x^{n}\right )^{\frac{1}{n}}} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.13717, size = 12, normalized size = 0.8 \begin{align*} \frac{x}{a^{\left (\frac{1}{n}\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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